Nah, player-led gyms make no sense at all. Let's say you own your own gym and you get challenged by an NPC. If you win, you get a little money like any other NPC battle. If you lose, you give this NPC a badge and...they disappear because they're just an NPC. It was a fruitless loss.

Let's add in Streetpass and say you challenge someone's gym. You lose, it's like any other loss. You win, you get...a badge? What kind of badge? Is this badge personalized to tailor to that specific person's gym? That results in an infinite number of badges. Do all Streetpass gyms give the same badge? That means you only need to battle one.

There's no suitable reward system if you win and no special outcome if you lose.